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3 years ago

PLEASE HELP!!! 15 PTS!!

Mathematics

1 answer:

kherson [118]3 years ago

6 0

Answer:

$\large\boxed{C.\ (2,\ -45^o)}$

Step-by-step explanation:

Regular coordinates (x, y)

Polar coordinates (r, φ)

$r=\sqrt{x^2+y^2}\\\\\psi=\arctan\frac{y}{x}$

We have the point

$(\sqrt2,\ -\sqrt2)$

Substitute:

$r=\sqrt{(\sqrt2)^2+(-\sqrt2)^2}=\sqrt{2+2}=\sqrt4=2\\\\\psi=\arctan\left(\frac{-\sqrt2}{\sqrt2}\right)=\arctan(-1)=-45^o$

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Which is an equivalent to to 752<br> O 1412<br> 021-10<br> 021-15

Stella [2.4K]

The answer to this equation is 1412 or 21-15

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3 years ago

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HELP ME <br> solve for the right triangle

VikaD [51]

Answer:

see explanation

Step-by-step explanation:

Using the cosine and tangent ratios in the right triangle

cos41° = $\frac{adjacent}{hypotenuse}$ = $\frac{VW}{VX}$ = $\frac{7}{VX}$

Multiply both sides by VX

VX × cos41° = 7 ( divide both sides by cos41° )

VX = $\frac{7}{cos41}$ ≈ 9.3

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tan41° = $\frac{opposite}{adjacent}$ = $\frac{WX}{VW}$ = $\frac{WX}{7}$

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7 × tan41° = WX, thus

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The sum of the 3 angles in a triangle = 180°

Subtract the sum of the given angles from 180° for ∠ X

∠ X = 180° - (90 + 41)° = 180° - 131° = 49°

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3 years ago

What is the perimeter of a square which has the same area as a circle with circumference of 4π?

Contact [7]

The circumference of a circle is given by: 2πr, where r is the radius of the circle. Equating 4π, we have 2πr = 4π so the radius of the circle is: r = 4/2 = 2. Then, the area of the circle is given by πr ^ 2 = π * (2 ^ 2) = 4π.Since the square and the circle have the same area, then: Let L be the side of the square, we have: L ^ 2 = 4π, clearing L = 2 * (π ^ (1/2))The perimeter of a square is the sum of its sides: P = L + L + L + L = 2 * (π ^ (1/2)) + 2 * (π ^ (1/2)) + 2 * (π ^ (1/2)) + 2 * (π) ^ (1/2)) P = 8 * (π ^ (1/2))

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3 years ago

Cathy borrows $3280 at 0.3% simple interest per month. When Cathy pays the loan back 9 years later, what is the total amount tha

Lisa [10]

Answer:

Step-by-step explanation:
Interest formula -
I = P × R × T
I = 3,280 × 0.3% × 9
What I basically did there wws multiply the amount of money, the simple interest, and the time.
Turn 0.3% into a decimal by dividing by a 100 which should give you 0.003

I = 3,280 × 0.003 × 9

Put that into a calculator, you get $88.56

Now, that's just the interest amount. Now you add it back to 3,280 to get the *total* amount.

3,280 + 88.56 = 3,368.56

Cathy ends us paying $3,368.56

Hope what I said made sense.

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2 years ago

What is the volume of the composite figure? (Round to the nearest hundredth. Use 3.14 for Pi.)

Natasha2012 [34]

The volume of composite figure is 385.17 cubic centimeters, if a half sphere and cone have a radius of 4 centimeters and height of 15 centimeters.

Step-by-step explanation:

The given is,

Composite figure is combination of a half sphere and cone

Both have a radius of 4 centimeters

The cone has a height of 15 centimeters

Step:1

Volume of composite figure = Volume of half sphere + Volume of cone

Step:2

Formula for volume of semi sphere,

$Volume of half sphere, V_{Half sphere} = \frac{2}{3} \pi r^{3}$

Where, r - Radius of Half sphere,

From given, r = 4 centimeters

$V_{Half sphere} = \frac{2}{3} \pi 4^{3}$

$= (0.6667) (3.14) (64)$ (∵ $\pi$ = 3.14 )

$V_{Half sphere}$ = 133.9733 cubic centimeters

Formula for volume of cone,

$Volume of cone, V_{cone} = \frac{1}{3} \pi r^{2} h$

where, r - Radius of cone

h - Height of cone

From given,

r = 4 centimeters

h = 15 centimeters

Volume of cone,

$V_{cone} = \frac{1}{3} \pi 4^{2}(15)$

$= (0.333333) (3.14)(16)(15)$ (∵ $\pi$ = 3.14 )

$V_{cone}$ $= 251.1997$ cubic centimeters

Step:3

Volume of composite figure = 133.9733 + 251.1997

Volume of composite figure = 385.17 cubic centimeters

Result:

The volume of composite figure is 385.17 cubic centimeters, if a half sphere and cone have a radius of 4 centimeters and height of 15 centimeters.

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3 years ago

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